assignment5_ProblemSet - subscript and use the same rule...

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ORIE 3300/5300 ASSIGNMENT 5 Fall 2008 Individual work. Due: 3 pm, Friday October 17. 1. Read Chapter 3 in the AMPL book, on transportation and assignment problems, in preparation for next week’s recitations. *Note: for the next few weeks, recitations will cover the material from Wednesday’s lab till the following Tuesday’s lab, rather than Monday to Friday. There is a lab on October 15th.* 2. (a) Introduce slack variables in the linear program below. Then solve it using the simplex method. Use the slacks as the initial basic variables. At each iteration, use the “smallest subscript rule”: whenever the simplex method allows you a choice between sev- eral possible entering variables, choose the one with the smallest
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Unformatted text preview: subscript, and use the same rule when the method allows you a choice between possible leaving variables. maximize 3 x 3 subject to-x 2 + x 3 ≤ x 2 + x 3 ≤ 2-x 1 + x 3 ≤ x 1 + x 3 ≤ 2 x 1 , x 2 , x 3 ≥ . (b) At which iterations was the basic feasible solution degenerate? (c) Which of the pivots you performed are degenerate? (d) Sketch a three-dimensional picture of the feasible region. (e) Which, if any, of the four ≤ constraints is “redundant”? In other words, which, if any, constraint could you delete without changing the feasible region? 1...
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